# Hoàng-Reed Conjecture

 Importance: High ✭✭✭
 Author(s): Hoang, Chinh T. Reed, Bruce A.
 Subject: Graph Theory » Directed Graphs
 Keywords:
 Posted by: fhavet on: March 11th, 2013
Conjecture   Every digraph in which each vertex has outdegree at least contains directed cycles such that meets in at most one vertex, .

This conjecture is not even known to be true for . In the case , Thomassen proved [T] that every digraph with minimum outdegree 2 has two directed cycles intersecting on a vertex.

This conjecture would imply the Caccetta-Häggkvist Conjecture.

## Bibliography

*[HR] C.T. Hoàng and B. Reed, A note on short cycles in digraphs, Discrete Math., 66 (1987), 103-107.

[T] C. Thomassen, The 2-linkage problem for acyclic digraphs, Discrete Math., 55 (1985), 73-87.

* indicates original appearance(s) of problem.